1. Field of the Invention
This invention relates to the analysis of the wavefront of a light beam.
2. Description of the Prior Art
Such a type of analysis makes it possible to test optical elements, as well as to qualify optical devices. It also allows for the study of non-directly measurable physical phenomena, such as optical index variations within turbulent media that can be encountered when crossing the earth atmosphere, as well as in a blowing vein. Numerous other applications could be contemplated such as metrology and the control of traditional or intense lasers.
The type of analysis of a wavefront according to this invention is based on the use of a diffraction grating positioned on the path of the beam to be analyzed.
For a better understanding of the following, such a grating is defined as being an optical system introducing periodic phase and intensity variations. Any grating is thus characterized by the multiplication of two functions: the one, referred to as phase function, represents the periodical phase variations introduced by the grating and the other one, referred to as intensity function, represents periodical intensity variations introduced by the grating.
In accordance to French patent 2 712 978, the Applicant reminds the mode of constitution and the definition of a two-dimensional grating. A set of points regularly arranged according to two directions constitutes a planar meshing. Such points define an elementary meshing. The elementary mesh is the smallest surface allowing one to achieve a non-lacunary paving of the plane. The polygon of the elementary mesh is the minimum surface polygon having the sides thereof supported by mediatrices of the segments connecting any point of the set to its nearest neighbors. A two-dimensional grating is the free repetition of an elementary pattern arranged according to a planar meshing. A planar meshing can define elementary meshes, being either hexagonal or rectangular (square meshes being only a special case for the latter).
When a diffraction grating is being illuminated with a light beam, referred to as an incident beam, the light beams being diffracted by the grating could be described as replicas of the incident beam. These beams are called sub-beams, each one corresponding to a diffraction order of the grating.
A particular optical processing of the thereby obtained sub-beams makes it possible to observe an interferogram (the interference image) made of a periodical meshing of light spots. If the incident wavefront is planar, the interferogram resulting from the interference of the sub-beams is referred to as an original interferogram. If the incident wavefront is not planar, the interferogram displays deformations with respect to an original interferogram; it is referred to as the deformed interferogram. Deformations of the deformed interferogram are sensitive to the increase rates of the wavefront.
The difference in level at one point P(x, y, z) of a surface S, du,d(P), is defined as being the difference in height z′ between two points, located on either side of point P, separated with a distance d along a direction u. As used therein, a difference in level of a surface along the direction u and at a distance d then means the set of points P′ (x, y, z′) resulting from the function du,d(P) applied to all points P of this surface. The set of points P′ defines a new surface, denoted S′.
The increase rate at one point P(x, y, z) of a surface S, tu,d(P), is defined as being the difference in level of du,d(P) obtained at such a point P divided by the distance d. The increase rate of a surface along the direction u and at a distance d is then used to mean the set of points P″ (x, y, z′/d) resulting from the function tu,d(P) applied to all points P of this surface. This set of points P″ defines a new surface, designated S″. When the surface S is continuous and if the distance d tends towards 0, then the surface S″ tends towards the gradient of S along the direction u. It is possible to find a sufficiently small distance d from which the increase rate of a continuous surface is very close to the gradient. In such a case, the gradient and the increase rate are assimilated.
In the field of the analysis of a wavefront, assimilating the increase rate to the gradient is very common (D. Malacara, “Optical Shop Testing”, Wiley-Interscience, 2nd Edition, pages 126-127).
For analyzing a wavefront, there is known a analyzer, referred to as the “Shack-Hartmann” analyzer, described in “Phase measurements systems for adaptive optics”, J. C. Wyant, AGARD Conf. Proc., No. 300, 1981. The general principle consists in optically conjugating the phase defect to be analyzed with a grid of micro-lenses. In the common plane of the micro-lens focuses, an intensity pattern comprising a deformed grating of spots as a function of the increase rate of the wavefront can be observed. An interpretation based on a subdivision into sub-beams diffracted by the micro-lens network has been developed in “Theoretical description of Shack-Hartmann wave-front sensor”, J. Primot, Optics Communications, 2003.
The so-called “Shack-Hartmann” wavefront analyzers have this advantage to operate with color beams. The color of a beam is defined as being a mix of monochromatic radiations of different wavelengths in fixed proportions. A monochromatic radiation should thus be considered as a particular color.
The light output of such analyzers is close to the maximum; in contrast, the sensitivity and the dynamics are only controllable by changing the micro-lens grid.
There are also known wavefront interferometric analyzers of the phase changing type, referred to as “phase-shifting” type, described in “Optical Shop Testing”, D. Malacara, Wiley-Interscience, 2nd Edition, chapter 14. The phase-shifting interferometry technique consists in temporally or spatially adding a known phase shift on one of the arms so as to determine the increase rate of a wavefront from several interferograms. Such a device, generally based on a Michelson type interferometer, is chromatic and can only simultaneously implement one single wavelength. It is however possible to successively use several wavelengths, as described in the above-mentioned work (page 560), so as to take profit of a larger measurement dynamics, and also to get rid of intensity offset errors in the light beams. A system combining a spatial phase-shifting interferometer and a two-wavelength measurement is described in the European patent 1 505 365.
In French patent applications 2 712 978 and 2 795 175, the Applicant described in particular three-wave and four-wave lateral shearing interferometers based on a diffraction grating and belonging to the family of shearing interferometers, a family distinct from the phase-shifting interferometers, and being the object of a description in chapter 4 of the above-mentioned work (“Optical Shop Testing”, D. Malacara, Wiley-Interscience, 2nd Edition, chapter 4).
According to the approach by splitting into sub-beams, the three-wave and four-wave lateral shearing interferometers, the diffraction grating optically splits the beam to be analyzed into three (three-wave lateral) or four (four-wave lateral) sub-beams.
A particular optical processing of thereby obtained sub-beams makes it possible to observe a interferogram comprising a periodic meshing of light spots and sensitive to increase rates of the wavefront.
In both above-mentioned patents of the Applicant, it is stated that such a result depends on the gradient, the situation being similar to the increase rate in the case of a continuous wavefront.
Analyzing increase rates can only occur with a possibility of continuous adjustment of the dynamics and the sensitivity. It is also possible to estimate the measurement error starting from the measurement itself; finally, the resulting interferogram is particularly adapted for analysis techniques based on Fourier transforms, providing it with simplicity and ease of implementation by computing means. Similarly as the Shack-Hartmann interferometer, such interferometers can operate with color beams and their light outputs are high.
Recently, new needs in the field of optics control have arisen. Increasingly high requirements in terms of radiometric sensitivity or spatial resolution result in achieving very large diameter optics made by applying elementary optics of a smaller size according to a Cartesian or hexagonal meshing. This is referred to as segmented optics. One well known example is the Keck telescope formed by applying thirty-six hexagonal elements. Such new optical systems require an adapted controlling means allowing for shaping the overall surface, i.e. the accurate positioning of the different segments so as to bring them all on one single surface.
On the other hand, opticians more and more often make use of so-called diffractive optical components, comprising alternated planar areas of different sizes and of different heights. These make it possible to implement optical functions similar to traditional components such as lenses and prisms, but with specific characteristics, in particular in the field of chromatics. Because of their particular shapes, such elements require adapted characterization means.
The common point of those two examples of application is the need to analyze a divided surface in order to map the position and height transitions, so as to determine the values thereof and/or to modify them, or to simply check them.
In the following, the expression “a divided surface” will be used for meaning the discontinuous application of surface parts, with possibly different sizes, with possibly voids between the parts and having differences in level between parts. As the divided surfaces are not continuous, the resulting surface of an increase rate operation could not be assimilated to the gradient.
The planar wavefront as reflected by a segmented mirror, the elementary segments of which have not been repositioned, or transmitted by a diffractive element such as above defined, are divided wavefronts. Those two examples of application thus show the interest of developing an analyzing means for a wavefront adapted for such new needs.
In the usual usage mode, the so-called “Shack-Hartmann” wavefront analyzers do not allow to analyze divided wavefronts.
J. C. Chanteloup, in the article “Multiple-wave lateral shearing interferometry for wave-front sensing”, Appl. Opt. 44, page 1559-1571 (2005) experimentally reported that three-wave and four-wave lateral shearing interferometers allowed for the analysis of divided surfaces having small difference in level with respect to the analysis wavelength. Analyzing divided wavefronts with differences in level higher than the analysis wavelength gives the correct position of the differences in level, but their height is undetermined as it is given at the nearest wavelength. Such a limitation is prohibitory for the above-mentioned applications.